Question

use the pythagorean theorem to find the distance between points p and q.
complete the equation to find c, the length of segment pq.
(type whole numbers.)
$c^2=(2)^2+(4)^2$
$c^2 = 4 + \square$

Explanation:

Step1: Recall the Pythagorean Theorem

The Pythagorean Theorem states that for a right triangle with legs of length \(a\) and \(b\), and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). In the given problem, we have \(a = 2\) and \(b=4\) (from the equation \(c^{2}=(2)^{2}+(4)^{2}\)).

Step2: Calculate \((4)^{2}\)

We know that \((4)^{2}=4\times4 = 16\). So the equation \(c^{2}=4+\square\) (where \(4=(2)^{2}\)) should have \(\square = 16\) because \(c^{2}=(2)^{2}+(4)^{2}=4 + 16\).

Step3: Find the value of \(c\) (optional, but to check)

If we want to find \(c\), we calculate \(c^{2}=4 + 16=20\), then \(c=\sqrt{20}=2\sqrt{5}\approx4.47\), but for the box in the equation \(c^{2}=4+\square\), we just need to find the value of \((4)^{2}\) which is 16.

Answer:

16